6.4 micrograms were administered to the patient.
The general form of this equation would be:
[tex]A=p(1+r)^t[/tex], where A is the total amount left, p is the initial amount, r is the rate of decay, and t is the number of time periods.
For our question, A =0.1 since that is the amount left; p is unknown; r is -0.5, since it loses half of its mass; and t will be 6. 2 hours = 120 minutes/20 minutes = 6 20-minute increments:
[tex]0.10 = p(1-0.5)^6
\\
\\0.10=p(0.5)^6[/tex]
Divide both sides by 0.5^6:
[tex]\frac{0.10}{0.5^6}=p
\\
\\6.4=p[/tex]
